WASHINGTON—Small banks are scoring big victories in their efforts to relax postcrisis rules by delivering a consistent message to lawmakers and policy makers: We’re not Wall Street.

Since the 2010 Dodd-Frank law ushered in a spate of new regulations, community bankers have fanned out across Washington to emphasize the differences between small “Main Street” banks focused on local lending and Wall Street firms they say are fixated on transaction volume. In conversations with lawmakers, small bankers argue many of the rules...